An object with a mass of $8 kg$ is acted on by two forces. The first is $F_1= < -9 N , 2 N>$ and the second is $F_2 = < 6 N, -3 N>$ . What is the object's rate and direction of acceleration?

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Answer 1 · 2018-01-31T15:11:13

The object's rate of acceleration is $=0.40ms^-2$ in the direction $198.4^@$ anticlockwise from the x-axis.

The resultant force is

$vecF=vecF_1+vecF_2 = <-9,2> + <6,-3>$

$= <-3, -1>$

The mass of the object is $m=8kg$

$vecF=mveca$

The acceleration is

$veca=1/mvecF=1/8* <-3, -1> = <-3/8, -1/8>$

The rate of acceleration is

$||veca||= ||<-3/8, -1/8>|| = sqrt((-3/8)^2+(-1/8)^2)$

$=sqrt(9/64+1/64)$

$=1/8sqrt10$

$=0.40ms^-2$

The direction is

$theta=180^@+arctan(1/3)=180+18.4=198.4^@$ anticlockwise from the x-axis.

An object with a mass of 8 kg8 kg is acted on by two forces. The first is F_1= < -9 N , 2 N>F_1= < -9 N , 2 N> and the second is F_2 = < 6 N, -3 N>F_2 = < 6 N, -3 N>. What is the object's rate and direction of acceleration?